Resistance of a conductor:
R = ρ × L ÷ A, with units that match

What resistivity tells you about a material

Resistance of a particular piece of wire depends on its shape, while resistivity is a property of the material itself. Copper, aluminium and steel each have a characteristic resistivity that is independent of how long or thick the conductor is. Shape then decides the actual resistance: long thin wires resist more than short thick ones.

The relationship is simple and intuitive. Double the length and the electrons have twice the distance to travel, so resistance doubles. Double the cross-sectional area and there are twice as many parallel paths for charge, so resistance halves.

Metals differ greatly. Silver is the best common conductor, copper follows closely, and aluminium is roughly one and a half times as resistive as copper. Steel is several times worse again, and alloys such as nichrome are chosen specifically because their high resistivity makes them good heaters.

Resistivity is also the reciprocal of conductivity. A material with high conductivity has low resistivity, so the two are two ways of expressing the same property.

The formula and getting the units right

Most mistakes happen in units. In strict SI, ρ is in ohm-metres, L in metres and A in square metres. Copper's resistivity is then about 1.75 × 10⁻⁸ Ω·m, and a 2.5 mm² cross-section is 2.5 × 10⁻⁶ m². Cable work is far easier with a practical set: ρ in Ω·mm²/m, L in metres and A in mm², which gives ohms directly.

The two forms are the same number: 1.75 × 10⁻⁸ Ω·m equals 0.0175 Ω·mm²/m because 1 m² is 10⁶ mm².

Worked example: 20 m of 2.5 mm² copper

Verifying in strict SI: 1.75 × 10⁻⁸ × 20 ÷ (2.5 × 10⁻⁶) = 0.14 Ω. Same answer, different units.

What does 0.28 Ω mean in use? With 10 A flowing, the voltage lost in the cable is 10 × 0.28 = 2.8 V. On a 230 V supply that is 1.2%, hardly noticeable. On a 12 V battery system it is 23%, which would starve the load.

A quick sanity check is available from the ratio. The wire is 20 m long and 2.5 mm² thick, so each metre needs 0.0175 ÷ 2.5 = 0.007 Ω. Twenty metres at 0.007 Ω gives 0.14 Ω, the same as before. Memorising the per-metre value for common sizes makes site estimates fast.

How thickness and material change the result

Aluminium has a higher resistivity than copper, so it needs a larger cross-section for equal resistance. The values above are typical room-temperature figures; handbooks and datasheets give exact numbers for the alloy and temper you are using.

The table also shows a pattern worth using. Going from 1.5 mm² to 2.5 mm² cuts resistance by 40%, and going to 4 mm² cuts it by 62.5%. The gains per step shrink as the cable gets thicker, so past a point the money is better spent elsewhere.

Using resistance to choose a cable

1. 1Decide the highest voltage drop you can accept, often given as a percentage of supply voltage.
2. 2Calculate the loop resistance from the round-trip length.
3. 3Multiply by the load current to get the drop and compare with the limit.
4. 4Increase the cross-section until the drop and the current rating are both satisfied.

Resistance sets energy loss too. The cable dissipates I² × R as heat, so 10 A through 0.28 Ω wastes 28 W, which is mostly harmless in air but significant in a bundle or conduit. Heating, not only voltage drop, often decides the minimum size.

As an illustration, take a 12 V load drawing 10 A over a 20 m run with a limit of 5% drop, which is 0.6 V. The loop resistance must not exceed 0.6 ÷ 10 = 0.06 Ω. The round trip is 40 m, so the required A is 0.0175 × 40 ÷ 0.06 = 11.7 mm², and the next standard size up would be chosen. Compare that with 2.5 mm² and it is clear why low-voltage cabling needs thick conductors.

Checking against a meter and knowing the limits

A low-resistance measurement needs a method that cancels the leads, such as a four-wire measurement, because test leads often add more than 0.1 Ω of their own. A basic multimeter can mislead on short runs.

• Stranded cable has the same cross-section in total but may have slightly higher effective resistance because of lay and gaps.
• Joints and terminations add small resistances that grow if loose or corroded.
• For alternating current at high frequencies, skin effect pushes current to the surface and raises effective resistance.
• Standards give tabulated resistances at 20 °C and 70 °C; use those for compliance work rather than this estimate.

An Ohm's law resistance tool handles the next step, relating the resistance you found to voltage and current, and is a convenient companion for the voltage-drop check.

Finally, keep proportion in mind. For a 20 m run of 2.5 mm² copper, the 0.14 Ω one-way resistance is tiny next to the load resistance of most mains appliances, which is why household wiring rarely needs this analysis. It becomes important for low-voltage, high-current systems, long runs and sensitive measurements, where the cable can rival the load itself.